Difference between revisions of "Livingson2006"
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{{BibEntry | {{BibEntry | ||
|BibType=ARTICLE | |BibType=ARTICLE | ||
| − | |Author(s)=Eric Livingston; | + | |Author(s)=Eric Livingston; |
|Title=The context of proving | |Title=The context of proving | ||
| − | |Tag(s)=EMCA; Mathematics; Proof; | + | |Tag(s)=EMCA; Mathematics; Proof; |
|Key=Livingson2006 | |Key=Livingson2006 | ||
|Year=2006 | |Year=2006 | ||
|Journal=Social Studies of Science | |Journal=Social Studies of Science | ||
|Volume=36 | |Volume=36 | ||
| − | |Pages= | + | |Number=1 |
| + | |Pages=39–68 | ||
|URL=http://journals.sagepub.com/doi/abs/10.1177/0306312705053055 | |URL=http://journals.sagepub.com/doi/abs/10.1177/0306312705053055 | ||
| + | |DOI=10.1177/0306312705053055 | ||
|Abstract=Discussions of mathematical problem-solving and heuristic reasoning have typically examined how proofs that are already known might be found. This approach has at least three problems: first, provers engaged in discovering proofs for themselves cannot have this perspective; second, if a proof is difficult, formulaic strategies quickly run out; third, beginning with a proof already in-hand separates reasoning about a proof from the actual circumstances in which such reasoning occurs. As an alternative approach to the study of mathematical reasoning, this paper presents a detailed descriptive account of the work of finding a specific proof, including the shifting of perspectives, the wrong paths, the mistakes and the outright errors. Even the appearance of a sketched diagram or of a course of mathematical writing can suggest unanticipated possibilities for finding a proof. This material is used to illustrate the paper’s central claim - that the ways that provers go about working on proofs provide the context for continuing that work and for discovering the reasoning that a particular proof is then seen to require. | |Abstract=Discussions of mathematical problem-solving and heuristic reasoning have typically examined how proofs that are already known might be found. This approach has at least three problems: first, provers engaged in discovering proofs for themselves cannot have this perspective; second, if a proof is difficult, formulaic strategies quickly run out; third, beginning with a proof already in-hand separates reasoning about a proof from the actual circumstances in which such reasoning occurs. As an alternative approach to the study of mathematical reasoning, this paper presents a detailed descriptive account of the work of finding a specific proof, including the shifting of perspectives, the wrong paths, the mistakes and the outright errors. Even the appearance of a sketched diagram or of a course of mathematical writing can suggest unanticipated possibilities for finding a proof. This material is used to illustrate the paper’s central claim - that the ways that provers go about working on proofs provide the context for continuing that work and for discovering the reasoning that a particular proof is then seen to require. | ||
}} | }} | ||
Latest revision as of 09:05, 13 November 2019
| Livingson2006 | |
|---|---|
| BibType | ARTICLE |
| Key | Livingson2006 |
| Author(s) | Eric Livingston |
| Title | The context of proving |
| Editor(s) | |
| Tag(s) | EMCA, Mathematics, Proof |
| Publisher | |
| Year | 2006 |
| Language | |
| City | |
| Month | |
| Journal | Social Studies of Science |
| Volume | 36 |
| Number | 1 |
| Pages | 39–68 |
| URL | Link |
| DOI | 10.1177/0306312705053055 |
| ISBN | |
| Organization | |
| Institution | |
| School | |
| Type | |
| Edition | |
| Series | |
| Howpublished | |
| Book title | |
| Chapter | |
Abstract
Discussions of mathematical problem-solving and heuristic reasoning have typically examined how proofs that are already known might be found. This approach has at least three problems: first, provers engaged in discovering proofs for themselves cannot have this perspective; second, if a proof is difficult, formulaic strategies quickly run out; third, beginning with a proof already in-hand separates reasoning about a proof from the actual circumstances in which such reasoning occurs. As an alternative approach to the study of mathematical reasoning, this paper presents a detailed descriptive account of the work of finding a specific proof, including the shifting of perspectives, the wrong paths, the mistakes and the outright errors. Even the appearance of a sketched diagram or of a course of mathematical writing can suggest unanticipated possibilities for finding a proof. This material is used to illustrate the paper’s central claim - that the ways that provers go about working on proofs provide the context for continuing that work and for discovering the reasoning that a particular proof is then seen to require.
Notes
